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THEORETICAL AND EXPERIMENTAL SELF-ASSEMBLY
by
Manoj Gopalkrishnan
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(COMPUTER SCIENCE)
December 2008
Copyright 2008 Manoj Gopalkrishnan

This thesis reports two contributions that have been prompted by a quest to better understand self-assembly.; Motivated by theoretical investigations of self-assembly, Adleman, Huang, Moisset, Reishus and I have investigated the mathematics of the "law of mass action." We believe that the law of mass action is of intrinsic mathematical interest, and may have deep connections to research in non-linear differential equations as well as algebraic geometry. One of our goals is to make the law of mass action available beyond chemistry. This has led us to a dynamical theory of sets of binomials over the complex numbers. A second goal is to present a mathematical consolidation of mass action chemistry. We have provided precise definitions, elucidated what can now be proved, and indicated what is only conjectured. This aspect of our work addresses the mathematical foundations of mass action chemistry.; My second contribution is to the emerging field of DNA self-assembly. It has been suggested that DNA self-assembly may lead to the manufacture of novel materials and computational devices. Chelyapov, Brun, Reishus, Shaw, Adleman and I have reported DNA complexes in the shape of triangles and in the pattern of hexagonal, planar tilings. Nikhil Gopalkrishnan, Adleman and I have reported DNA complexes in the shape of cylinders and Mobius strips. The prevalent practice in the DNA self-assembly community appears to be to model DNA double helices as rigid cylinders and DNA lattices as rigid sheets. In contrast, our nanostructures were designed to avail of residual flexibilities in DNA double helices and DNA lattices.

THEORETICAL AND EXPERIMENTAL SELF-ASSEMBLY
by
Manoj Gopalkrishnan
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(COMPUTER SCIENCE)
December 2008
Copyright 2008 Manoj Gopalkrishnan